While looking at Tao’s post on the law of large numbers, I claimed to Alap that Markov’s inequality was “obvious”. Asked to back that up, though, I couldn’t remember why it was obvious. Take some distribution . For simplicity, assume this distribution is over the non-negative reals. Then, Markov’s inequality states, for

.

Though I find it more intuitive in the form

.

Now, a proof is pretty trivial, basically by writing down the definitions of both sides.